A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors

Zhang, Tengfei; Lewis, E. E.; Smith, M. A.; Yang, W. S.; Wu, Hongchun

doi:10.1080/00295639.2016.1273023

Title: A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors

Abstract

A two-dimensional/one-dimensional (2D/1D) variational nodal approach is presented for pressurized water reactor core calculations without fuel-moderator homogenization. A 2D/1D approximation to the within-group neutron transport equation is derived and converted to an even-parity form. The corresponding nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal functions in z are used to approximate the spatial flux distribution. On the radial interfaces, orthogonal polynomials are employed; on the axial interfaces, piecewise constants corresponding to the finite elements eliminate the interface homogenization that has been a challenge for method of characteristics (MOC)-based 2D/1D approximations. The angular discretization utilizes an even-parity integral method within the nodes, and low-order spherical harmonics (P_N) on the axial interfaces. The x-y surfaces are treated with high-order P_N combined with quasi-reflected interface conditions. Furthermore, the method is applied to the C5G7 benchmark problems and compared to Monte Carlo reference calculations.

Authors:

Zhang, Tengfei ^[1]; Lewis, E. E. ^[2]; Smith, M. A. ^[3]; Yang, W. S. ^[4]; Wu, Hongchun ^[1]

Xi'an Jiaotong Univ., Xi'an, Shannxi (China)
Northwestern Univ., Evanston, IL (United States)
Argonne National Lab. (ANL), Lemont, IL (United States)
Purdue Univ., West Lafayette, IN (United States)

Publication Date:: Tue Apr 18 00:00:00 EDT 2017

Research Org.:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Nuclear Energy (NE); USDOE Office of Science (SC), Basic Energy Sciences (BES); National Natural Science Foundation of China (NSFC)

OSTI Identifier:: 1374150

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: Nuclear Science and Engineering

Additional Journal Information:: Journal Volume: 186; Journal Issue: 2; Journal ID: ISSN 0029-5639

Publisher:: American Nuclear Society - Taylor & Francis

Country of Publication:: United States

Language:: English

Subject:: 21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS; 2D/1D variational nodal method; eliminating the interface homogenization

Citation Formats


                    Zhang, Tengfei, Lewis, E. E., Smith, M. A., Yang, W. S., and Wu, Hongchun. A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors.  United States: N. p., 2017. 
Web.  doi:10.1080/00295639.2016.1273023.

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                    Zhang, Tengfei, Lewis, E. E., Smith, M. A., Yang, W. S., & Wu, Hongchun. A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors.  United States.  https://doi.org/10.1080/00295639.2016.1273023

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                    Zhang, Tengfei, Lewis, E. E., Smith, M. A., Yang, W. S., and Wu, Hongchun. Tue .  
"A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors".  United States.  https://doi.org/10.1080/00295639.2016.1273023.  https://www.osti.gov/servlets/purl/1374150.

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@article{osti_1374150,

  title        = {A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors},

  author       = {Zhang, Tengfei and Lewis, E. E. and Smith, M. A. and Yang, W. S. and Wu, Hongchun},

  abstractNote = {A two-dimensional/one-dimensional (2D/1D) variational nodal approach is presented for pressurized water reactor core calculations without fuel-moderator homogenization. A 2D/1D approximation to the within-group neutron transport equation is derived and converted to an even-parity form. The corresponding nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal functions in z are used to approximate the spatial flux distribution. On the radial interfaces, orthogonal polynomials are employed; on the axial interfaces, piecewise constants corresponding to the finite elements eliminate the interface homogenization that has been a challenge for method of characteristics (MOC)-based 2D/1D approximations. The angular discretization utilizes an even-parity integral method within the nodes, and low-order spherical harmonics (PN) on the axial interfaces. The x-y surfaces are treated with high-order PN combined with quasi-reflected interface conditions. Furthermore, the method is applied to the C5G7 benchmark problems and compared to Monte Carlo reference calculations.},

  doi          = {10.1080/00295639.2016.1273023},

  journal      = {Nuclear Science and Engineering},

  number       = 2,

  volume       = 186,

  place        = {United States},

  year         = {Tue Apr 18 00:00:00 EDT 2017},

  month        = {Tue Apr 18 00:00:00 EDT 2017}

}

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https://doi.org/10.1080/00295639.2016.1273023

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Works referenced in this record:

A First Course in Finite Elements
book, January 2007

Fish, Jacob; Belytschko, Ted
DOI: 10.1002/9780470510858

Works referencing / citing this record:

Improved Accuracy in the 2-D/1-D Method with Anisotropic Transverse Leakage and Cross-Section Homogenization
journal, September 2018

Jarrett, Michael; Kochunas, Brendan; Larsen, Edward
Nuclear Science and Engineering, Vol. 192, Issue 3
DOI: 10.1080/00295639.2018.1507186

Generalized Partitioned Matrix Acceleration for Variational Nodal Diffusion Method
journal, January 2019

Wang, Yongping; Li, Yunzhao; Zhang, Tengfei
Nuclear Science and Engineering, Vol. 193, Issue 6
DOI: 10.1080/00295639.2018.1542883

An Overview of AI Methods for in-Core Fuel Management: Tools for the Automatic Design of Nuclear Reactor Core Configurations for Fuel Reload, (Re)arranging New and Partly Spent Fuel
journal, July 2019

Nissan, Ephraim
Designs, Vol. 3, Issue 3
DOI: 10.3390/designs3030037

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Title: A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors

Abstract

Citation Formats

A First Course in Finite Elements book, January 2007

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book, January 2007

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